Suppose that X is a geometric random variable. (a) prove that for positive integers n and k, P(X=n+k|X>n)=P(X=k). (b)explain what this result means and why it makes sense for a geometric distribution to have this property.

A quiz consists of 20 multiple-choice questions, each with 5 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 60%.

You learn that the data is actually a sample from the U.S. population where 1000 people were surveyed from each state and the percentage reflects the percentage of the sample who completed 4 years of college (bachelor's degree).

The number of students who belong to the dance company at each of several randomly selected small universities is shown below. Estimate the true population mean size of a university dance company with 99% confidence. Show step by step.

A new phone answering system for a company is capable of handeling seven calls every 10 minutes. Prior to installing the new system, company analyst determined that the incoming calls to the system are Poisson distributed with a mean of four every

The average length of life of a brand of light bulb is 2000 hours with a population standard deviation of 120. A sample of 100 light bulbs is to be taken. What is the probability of the sample mean being less than 2020 hours? P(xbar< 2020)

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